Luis Suarez missed the biggest chance of the first half, his attempt from close range only finding the side netting.
It appeared his team would cope without him before the Atletico Madrid defender put a bullet header into the net for the victor on 89 minutes.
"I can nearly assure you 100% he will play, save unforeseen circumstances at the very last minute", said Cuper.
"He's recovered very, very quickly - we've paid a lot of attention to him", the veteran coach told a news conference before the squad's last training session ahead of Friday's match.
The 25-year-old injured shoulder ligaments in the Champions League final defeat by Real Madrid on May 26 and has not played since. "We always know we're running a risk when playing a match, that's something we can't hide [from]".
Egypt's Group A schedule kicks off on June 15 against Uruguay, followed by Russian Federation on June 19 and Saudi Arabia on June 25.More news: I defend North Korea's human rights record to help avoid nuclear attack
Most expect Uruguay to dominate this game in all aspects, including both corners and chances created, which should see them spend much of their time in Egypt's half.
The game between Uruguay and Egypt is highly anticipated with latter team because the country will come off a virtual gridlock and now to their first FIFA World Cup match in almost three decades drought.
Today's game will see the 71-year-old take charge of the famously tournament-tough South American side at his fourth World Cup finals, the first being back in 1990.
Disappointingly, we won't be forced to listen to "Robbie Williams's greatest hits, featuring Opera Lady" today and instead there will be no grand ceremony. "Even though we did not win, we hope we will have better results in the future".
The result sees the South Americans draw level with Russian Federation on three points at the top of Group A. The work we do all the time is precisely to make our players understand that they have to work harder.
Suarez looked a shadow of that player in his Russian Federation 2018 debut, and not just because he kept his teeth to himself.
They were impressive at the 2010 World Cup, where they finished fourth.